Property: Simplifying Square Roots

To simplify $$\sqrt{a \cdot b}$$ , use $$\sqrt{a} \cdot \sqrt{b}$$ .

Property: Simplifying Cube Roots

To simplify $$\sqrt[3]{a \cdot b}$$ , use $$\sqrt[3]{a} \cdot \sqrt[3]{b}$$ .

Example: Simplifying $$\sqrt{50}$$

$$\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$$ .

Example: Simplifying $$\sqrt{12}$$

$$\sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}$$ .

Example: Simplifying $$\sqrt{a^2}$$

$$\sqrt{a^2} = a$$ (if a >= 0).

Example: Simplifying $$\sqrt{g^4}$$

$$\sqrt{g^4} = g^2$$ (if g >= 0).

Definition: Radical Expression

An expression that includes a root, such as a square root or cube root.

Definition: Perfect Square

A number that can be expressed as the square of an integer.

Algebra 1 Team Decathlon -- Event #4 High Jump Flashcards

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Definition: Square Root

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Definition: Cube Root

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